Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this talk, we compare three sequent calculi for bi-intuitionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion...

Recently, magnetic tunnel junction (MTJ)-based implication logic gates have been proposed to realize a fundamental Boolean logic operation called material implication (IMP). For given MTJ characteristics, the IMP gate circuit parameters must be optimized to obtain the minimum IMP error probability. In this work we present the optimization method and investigate the effect of MTJ device paramete...

It is shown that it is possible to regard stochastic and fuzzy logics as being derived from two different constraints on a probability logic: statistical independence (stochastic) and logical implication (fuzzy). To contrast the merits of the two logics, some published data on a fuzzylogic controller is reanalysed using stochastic logic and it is shown that no significant difference results in ...

At first, George Boole introduced conditional propositions as the basis for better development of propositional logic. A compound statement composed two atomic statements (antecedent and consequent) by connective 'if—then' is called For example: "If it raining, then roads are wet". Here first this proposition, 'It raining,' antecedent, second, 'the wet,' consequent. The material in which false ...

In [5] it is shown how a model for the logic of constructible duality is a symmetric monoidal closed category with products, that is, a model of linear logic. Remarkably, Nelson’s strong negation∼ behaves as linear duality ⊥. We compare it with some previous results from [4] regarding stable models in a linear logic setting, and suggest some further lines to explore. 1. From Ncd to linear logic...

suhrawardi’s logic of the hikmat al-ishraq is basically modal. so to understand his modal logic one first has to know the non-modal part upon which his modal logic is built. in my previous paper ‘suhrawardi on syllogisms’(3) i discussed the former in detail. the present paper is an exposition of his treatment of modal syllogisms. on the basis of some reasonable existential presuppositions and a...

This paper introduces the logics of super-strict implications, where a implication is strengthening C.I. Lewis' strict that avoids not only paradoxes material but also those implication. The semantics implications obtained by (normal) relational for We consider all are based on frames modal in cube. it shown connexive they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theore...

in this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. it would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. we give the main properties of the operations defined and prove som...